A Robust Numerical Method for a Singularly Perturbed Fredholm Integro-Differential Equation

An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation

“…Proof. The proof is done by similar approach as in [5,12]. Now, we turn to establishment of the difference scheme.…”

“…Delay forms of SPVIDEs were discretized in [21,35]. Amiraliyev et al recently constructed an exponential-difference scheme with an accuracy of O N −1 for the first-order linear singularly perturbed Fredholm integro-differential equation (SPFIDE) on a uniform grid in [1], and finite difference scheme with an accuracy of O N −2 ln N on a Shishkin grid for the second-order linear SPFIDE in [12]. The first and the second order difference schemes were proposed in [4,34].…”

Numerical Solution of a Singularly Perturbed Fredholm Integro Differential Equation with Robin Boundary Condition

“…Using the appropriate quadratures formulas with the remainder term in integral form [4,12,17,27] (see also [24], pp. 207-214), to the first term at the right side of (2.3) we get…”

An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition

“…Amiraliyev et al [ 3 , 5 ] proposed an exponentially fitted difference method on a uniform mesh for solving first and second-order linear SPFIDEs, demonstrating that the approach is first-order convergent uniformly in . Difference schemes of the fitted homogeneous type with an accuracy of on a piecewise uniform mesh for this type of problems are given in [ 4 , 15 ]. It should also be noted that in [ 30 , 31 ], for the numerical solution of singularly perturbed Volterra integro-differential equations, first-order difference schemes on a piecewise uniform mesh are given, followed by Richardson extrapolation to obtain the second order of accuracy.…”